This invention generally relates to the field of optical measuring and testing and more specifically to apparatus for using interference fringe patterns for position encoding. There are two basic methods for producing fringe patterns: (1) an interferometric technique that utilizes interference phenomena, and (2) a Moire technique that utilizes shadow casting and/or pattern multiplication.
There are a wide variety of measuring and testing procedures that utilize interference fringe patterns and there are many ways to produce and control interference fringes. Generally, an interference fringe pattern is produced when at least two coherent beams of light are brought together and interact. When two coherent beams interact, they destructively interfere to produce dark spots or bands and constructively interfere to produce bright spots or bands.
Moire fringes are produced when two similar, geometrically regular patterns consisting of well defined clear and opaque areas are juxtaposed and transilluminated. Some examples of geometrically regular patterns used to generate Moire fringes include (1) Ronchi rulings, (2) sets of concentric circles, and (3) radial grids. The generation of Moire fringes can be considered as shadow casting; that is, the shadow of the first pattern falling onto the second pattern produces the Moire fringes. The mathematical function describing Moire fringes is obtained by multiplying the intensity transmissions or irradiances of the overlapped geometrically regular patterns.
Apparatus using Moire or interferometric techniques is used to position accurately two elements relative to each other. With interferometric techniques, an incoming beam of light is generally split into two parts. One part is reflected from a reference position; the other, from a movable element. The reflected beams are recombined to produce an output fringe pattern that "moves" as the movable element moves. In one example of a Moire technique, two high contrast Ronchi rulings of slightly different spatial frequencies are juxtaposed and transilluminated. One ruling is stationary while the other is movable in a predetermined plane. Photodetectors sense the variations in the light that passes through the gratings and produce signals that indicate the motion.
Certain disadvantages exist in apparatus that utilizes the interferometric techniques to form fringe patterns in position detection applications. For example, in such apparatus the two light beams generally travel through different light paths that contain distinct optical elements. If the elements in each path are not matched optically, aberrations distort the fringe pattern. Matched optical elements can eliminate the aberration problem; however, they significantly increase the overall expense of the apparatus. Moreover, this apparatus is subject to various outside influences, such as vibration and thermal change. These influences can cause fringe pattern motion or noise and lead to improper measurements.
Moire techniques also have many limitations. When small spacings and high accuracies are required, the geometrically regular patterns used to generate Moire fringes are quite difficult and expensive to produce. In applications where one ruling moves next to a fixed ruling, the spacing between the rulings must be held constant or errors result. Also, Moire fringes are localized, i.e., they exist in a very small region of space, and additional optical components are often required to image the Moire fringes into desired regions.
Recently, an amplitude grating and a spatially coherent, quasi-monochromatic light source have been used to generate interference fringes. An amplitude grating is a generally transparent to semi-transparent media whose opacity is altered in accordance with some spatially periodic pattern. An amplitude grating "breaks up" or diffracts an incoming beam of light into a series of diffracted cones or orders. The strength, or amount, of light in each order depends upon the exact shape of the periodic opacity of the amplitude grating. Although various diffracted orders could be approximately the same strength, scalar diffraction theory for a thin amplitude grating predicts that the dominant strength will lie in the zero order undiffracted light and that the strength of other diffracted orders will vary. Indeed, practical applications bear out this prediction.
In the apparatus in U.S. Pat. No. 3,738,753, issued June 12, 1973, light passes from a source through an amplitude grating to produce different order cones of diffracted light: for example, zero order and first order cones. To compensate for the different intensities, the diffracted light cones are reflected back through the grating. After the second passage through the grating, the zero order cone of the reflected first order cone and the first order cone of the reflected zero order cone have equal strengths and are combined to form a high contrast interference fringe field. This double pass system is quite stable because it closely approximates a common path interferometer. In a common path interferometer the interfering beams traverse the same optical path. Therefore, perturbations affect both beams simultaneously and do not distort the output fringe pattern which is sensitive only to differences between the two optical paths. However, problems in such a double pass system do occur because it is difficult to control grating substrate aberrations and mirror-grating separation.
Further improvements have been made with the advent of holographically produced amplitude gratings. Holographic amplitude gratings are produced by exposing a high resolution photographic emulsion to the precise interference pattern of a laser two-beam interferometer. During ordinary photographic processing, the photosensitive silver halide in the emulsion converts into opaque metallic silver to form the amplitude grating.
In U.S. Pat. No. 3,829,219, issued 1974 to Wyant, and U.S. Pat. No. 4,118,124 issued Oct. 3, 1978 to Matsuda, one such holographic grating, a double frequency holographic grating, produces a so-called "shearing" pattern. This grating is produced by sequentially exposing a single photographic emulsion to a first laser interference pattern of a first spatial frequency, f.sub.1, and then to a second laser interference pattern of a second spatial frequency, f.sub.2. Equal amplitude transmission modulations at both frequencies f.sub.1 and f.sub.2 are achieved by adjusting the exposure to the first and second laser patterns. Ordinarily, the two sequential exposures are identical, but if f.sub.1 and f.sub.2 are very different or if one laser pattern is in red light and the other is in green light, the sequential exposures must be compensated for the spectral and frequency responses of the photographic plate. These exposure adjustments to achieve equal amplitude transmission modulations in f.sub.1 and f.sub.2 are usually done by trial and error.
Upon illumination with spatially coherent, quasimonochromatic light, this double frequency grating produces two first order light cones of equal strength, one light cone being associated with each of the f.sub.1 and f.sub.2 frequencies. These two first order light cones interact to form a very stable, high contrast fringe pattern. Such a double frequency holographic shearing interferometer also is a common path interferometer. It is simple to construct. However, in this interferometer it is necessary to separate the zero order cone from the interacting first order cones. This separation requirement limits the f/number of the input light cone and the amount of shear obtainable. Moreover, if the two first order cones have high diffraction angles an astigmatic distortion of the output fringe field exists. In addition, the efficiency, or ratio of output fringe field power to input power, is only about 2%.
For many years people have bleached photographically recorded amplitude gratings to obtain "phase gratings". One basic type of such bleaching, known as volume bleaching, chemically converts the opaque silver in the photographic emulsion into a transparent, high index silver salt. A second type of bleaching, known as tanning, chemically removes the developed silver within the emulsion and leaves a void. A tanned phase grating has a corrugated surface. Whereas an amplitude grating selectively absorbs light, a bleached phase grating selectively introduces phase delays across the input light beam. As a result, a phase grating is much more efficient than an amplitude grating; that is, the ratio of first order power to input power is greater.
However, bleached gratings are generally characterized by substantial problems. They are very noisy and also may deterioriate physically back into amplitude gratings upon extended exposure to light. Bleached gratings also have a lower spatial frequency response than amplitude gratings. Although volume bleached gratings are less noisy and have a higher spatial frequency response than their tanned counterparts, they generally are weaker and less efficient.
The efficiency of a volume bleached grating can be increased by increasing its thickness. However, any substantial increase in thickness drastically changes the basic diffraction properties of the grating. Any amplitude or phase grating can be considered optically thick when the optical thickness of the emulsion is more than five times the grating spacing. A grating can be considered optically thin if the optical thickness of the emulsion is less than half the grating spacing. Properties of thick gratings are accurately predicted by electromagnetic theory while properties of thin gratings are described by scalar diffraction theory. For example, a thick phase grating output consists of only the zero order and one first order diffracted cone. In addition, diffraction takes place only for a plane wave input at a certain specified angle with respect to the grating. On the other hand, a thin grating of the same spacing produces multiple orders (i.e. the 0, .+-.1, .+-.2, .+-.3, etc. orders) with either a spherical wave or plane wave input at an arbitrary angle with respect to the grating.
Distinctions between optically thin amplitude and optically thin phase gratings are accurately predicted by scalar diffraction theory. When a pure sinusoidal amplitude transmission perturbation exists in a thin amplitude grating, only the zero and .+-.1 diffracted orders exist. When a pure sinusoidal phase perturbation occurs in a thin phase grating, many orders (e.g., the 0, .+-.1, .+-.2, .+-.3, and other orders) are observed. The strengths of the phase grating orders are proportional to the normalized Bessel functions [J.sub.n (m/2)].sub.2, where n is the order number (e.g., n equals 0, .+-.1, .+-.2, . . . ) and m is the strength or size of the phase perturbation in radians. When the amplitude grating perturbation departs from a pure sinusoidal form, additional diffracted orders are generated. The strengths of these additional orders are directly related to the strengths of the Fourier components associated with the grating perturbation function.
With a phase grating, the diffracted orders associated with a non-sinusoidal phase perturbation are predicted by convolving the individual outputs from each Fourier component of the phase perturbation. Such a multiple convolution reveals complicated phase relationships between multiple orders associated with just one particular Fourier component. In addition, diffracted orders corresponding to sum and difference frequencies are generated when the phase perturbation consists of more than one fundamental spatial frequency. For example, one might consider bleaching the previously discussed double-frequency holographic grating to improve its poor efficiency. Although bleaching will increase the overall efficiency of such a grating, the bleached grating, in accordance with the convolutional operation, produces sum and difference frequency diffraction cones that are in addition to and that interact with the desired fundamental frequency diffraction cones. It is then possible for the sum and difference frequency diffraction cones to destroy the fringe field.
Therefore, it is the object of this invention to provide an improved holographic phase grating for producing a high contrast interference pattern.
Another object of this invention is to provide an improved holographic grating that is useful in a number of applications including position detection.
Yet another object of this invention is to provide apparatus for accurate detection of position information.